The work of J Ross describes the Comet 39P/Oterma orbit as being a comet which changed its orbit quite dramatically after a close encounter with Jupiter . This happened more than 40 years ago . Ths comet was discovered in 1942. Now the comet orbits in a 3:2 resonance outside Jupiters orbit , but some 45 years ago it was in a 2:3 resonace orbit in the inner solar system . It must have passed through the L1 point of Jupiter towards the L2 point , ejecting him into the outer solar system in his present 3:2 resonance. The animation herunder shows 16 frames , each covering 10 years . Animation goes back in time . (rotating frame to Jupiter ) The last picture is the total path of the comet over a period of 100 years from now in top view, sun centered . As can be seen in the last pcture the comet must have changed its orbit even twice ( if the accurancy of the simulation allows this statement ) .

The next frames show the comets orbit , centered on Jupiter , at the time of closed approach. Animation is this time forward in time . The grey orbit depicts the orbit of Jupiters outerst biggest moon Callisto . According to the timer on the screen the closest approach must have been january 1963. L1 must be on the left , L2 on the right of Jupiter as the comet is heading towards the outer solar system.

From the viewpoint of the Sun the 1963 manouever must have looked as following : Oterma approaches from under , gets close to the L1 point ( if it was right on the L1 point it had to be just in front of Jupiter ) , gets to the L2 point and leaves to the left , meaning it moves slower than Jupiter as it is ejected in the "outer" solar solar system . The white orbit is Callisto's orbit .

As Oterma is a comet and is currently residing between Saturn and Jupiter , where does it come from and how did it come here ? Has it taken the "highway" jumping from Neptune to Uranus to Saturn to Jupiter ...? To find out I ran the simulations backwards and found that for a long time ( several thousands of years ) Oterma can have been in an moderate elliptical orbit between Jupiter and Saturn , its orbit crossing Jupiters and Saturn twice ! Of course such an orbit is unstable . Some 6000 years ago Oterma meets Saturn very closely and is ejected in a highly eccentric orbit bringing it far beyond Pluto and inside Jupiters orbit with period of about 200 years . Of course such a simulation has the disadvantage of accumulating errors over time but it shows a possible scenario . Here's the evolution of its period related to Jupiters .

The slingshot in post #3 in anaglyph looks as following . The comet approaches from the left , makes a 180 turn and leaves Jupiter towards the outer solar system . Picture was generated with a PBasic postgenerator .